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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 163 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.7x + 3y = 10 and 3x + 7y = 10 →
  2. 2.2x + y = 12 and x − 5y = −5 →
  3. 3.x − 3y = −4 and 2x + 4y = 22 →
  4. 4.2x + 2y = −12 and 5x + y = −26 →
  5. 5.2x + 4y = 38 and 5x + 3y = 32 →
  6. 6.3x + 6y = −9 and 3x − 5y = 46 →
  7. 7.3x − 6y = −3 and 4x + y = −13 →
  8. 8.5x + 2y = 20 and 2x + 5y = 29 →
  9. 9.3x + 8y = 57 and 8x + 3y = −13 →
  10. 10.5x + 3y = −66 and 3x + 5y = −62 →
  11. 11.4x + 2y = 32 and 2x + 4y = 28 →
  12. 12.x + 5y = −13 and 4x − 5y = −27 →
  13. 13.3x + 6y = −42 and 6x + 3y = −12 →
  14. 14.x + 6y = 12 and 5x + y = 31 →
  15. 15.3x − 6y = −6 and x − 4y = −6 →
  16. 16.2x + 5y = 17 and 5x + 2y = 11 →
  17. 17.5x + 2y = 32 and 2x + 6y = −8 →
  18. 18.x + 9y = 54 and 9x + y = −74 →
  19. 19.2x + 5y = 26 and 6x + 5y = 38 →
  20. 20.5x + 8y = 101 and 8x + 5y = 107 →
  21. 21.3x + 2y = 28 and 2x + 3y = 32 →
  22. 22.x + 4y = 8 and 3x + 2y = 14 →
  23. 23.x + 4y = 6 and 4x + y = −6 →
  24. 24.3x + 2y = 28 and 6x + 5y = 58 →
  25. 25.9x + 4y = 55 and 4x + 9y = 10 →
  26. 26.x + 2y = 14 and 2x + y = 19 →
  27. 27.6x + 5y = 37 and 2x − 5y = 19 →
  28. 28.2x + 3y = 9 and 2x − 5y = 17 →
  29. 29.5x + 3y = 59 and 3x + 5y = 61 →
  30. 30.8x + 7y = −41 and 7x + 8y = −34 →
  31. 31.2x + 4y = 30 and 2x − 3y = 9 →
  32. 32.6x + y = 28 and 4x + 6y = 40 →
  33. 33.x − 6y = 31 and 5x + 6y = 11 →
  34. 34.4x + 3y = 24 and 5x + 3y = 33 →
  35. 35.4x + 6y = 26 and 6x + 4y = 24 →
  36. 36.9x + 5y = 43 and 5x + 9y = −1 →
  37. 37.3x + y = −19 and 6x + 3y = −42 →
  38. 38.5x + 6y = −9 and 6x − 5y = −84 →
  39. 39.5x + y = 40 and 5x + 4y = 25 →
  40. 40.3x + y = 20 and x + 3y = 20 →

Answer key

  1. x = 1, y = 1
  2. x = 5, y = 2
  3. x = 5, y = 3
  4. x = −5, y = −1
  5. x = 1, y = 9
  6. x = 7, y = −5
  7. x = −3, y = −1
  8. x = 2, y = 5
  9. x = −5, y = 9
  10. x = −9, y = −7
  11. x = 6, y = 4
  12. x = −8, y = −1
  13. x = 2, y = −8
  14. x = 6, y = 1
  15. x = 2, y = 2
  16. x = 1, y = 3
  17. x = 8, y = −4
  18. x = −9, y = 7
  19. x = 3, y = 4
  20. x = 9, y = 7
  21. x = 4, y = 8
  22. x = 4, y = 1
  23. x = −2, y = 2
  24. x = 8, y = 2
  25. x = 7, y = −2
  26. x = 8, y = 3
  27. x = 7, y = −1
  28. x = 6, y = −1
  29. x = 7, y = 8
  30. x = −6, y = 1
  31. x = 9, y = 3
  32. x = 4, y = 4
  33. x = 7, y = −4
  34. x = 9, y = −4
  35. x = 2, y = 3
  36. x = 7, y = −4
  37. x = −5, y = −4
  38. x = −9, y = 6
  39. x = 9, y = −5
  40. x = 5, y = 5

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